[Insight-developers] Default boundary condition for WindowedSinc as constant?

[Bradley Lowekamp]

Hello Nick,

Thanks for getting back to me on this.

I also ran the Sinc interpolators on a constant image, and I got a larger error than expected. The following Python code was run with the ZeroFlux boundary condition and the radius template parameter of 5:

# Create a image of all ones
img = sitk.Image( 10, 10 , sitk.sitkFloat64 )
img += 1

iterps = [sitk.sitkNearestNeighbor,
          sitk.sitkLinear,
          sitk.sitkBSpline,
          sitk.sitkGaussian,
          sitk.sitkHammingWindowedSinc,
          sitk.sitkCosineWindowedSinc,
          sitk.sitkWelchWindowedSinc,
          sitk.sitkLanczosWindowedSinc,
          sitk.sitkBlackmanWindowedSinc]

for i in iterps:
    eimg= sitk.Expand( img, [10,10], i )
    print "RMS:",(sum( (1-eimg)**2)/len(eimg))**.5, "Abs:", max(sitk.Abs(1-eimg))

RMS: 0.0 Abs: 0.0
RMS: 0.0 Abs: 0.0
RMS: 1.90178968104e-16 Abs: 5.55111512313e-16
RMS: 0.0 Abs: 0.0
RMS: 0.00519432546396 Abs: 0.007170554427
RMS: 0.00111584107245 Abs: 0.00190357704047
RMS: 0.000697067283848 Abs: 0.00118879124085
RMS: 0.00143647177089 Abs: 0.00245097611656
RMS: 0.000491351024756 Abs: 0.000833429218405

Skimming through the code it looks like the kernel is point sampled and not integrated over the pixel. I wonder if that is the issue.

Brad

On Dec 18, 2012, at 3:03 PM, Nicholas Tustison <ntustison at gmail.com> wrote:

> Hi Brad,
> 
> Yeah, we just use the default.  We've probably never noticed it since,
> as you say, we typically are interpolating a blob in the middle of a black
> background.
> 
> I think Paul Yushkevich wrote those windowed sinc interpolators.  You 
> might want to ask him why they're the default.
> 
> Nick
> 
> 
> 
> On Dec 18, 2012, at 1:09 PM, Bradley Lowekamp <blowekamp at mail.nih.gov> wrote:
> 
>> Hello,
>> 
>> As I am finally integrating the different interpolators into SimpleITK. I am giving them a close look over.
>> 
>> The set of WindowSincInterpolateImageFunctions takes a Boundary condition template parameter. This defaults to ConstantBoundaryCondition. That is by default the pixels are zero outside the image, and they are not zero flux. This results in quite a bit of ringing and fading around my test images. It seems just wrong.
>> 
>> I can easily specify this parameter as the ZeroFluxNeumannBoundaryCondition (I don't think we have a mirror/reflective boundary, which is another possibility), and things look quite good and as I expect the output to be. I was curious as to what others were doing so I perused BRAINS and ANTS, grepping for the sinc interpolator. And to my surprise they are using the default!
>> 
>> Is there a reason that this default is preferred? Or is it that I am not processing a single blob in the center of a black image (aka a brain)?
>> 
>> Also in terms of consistency across the interpolators, this is the only one which takes a boundary condition template parameters. The other interpolators appear to behave sensibly, and exhibit a zero-flux type boundary condition. I think the default for this may need to be changed.
>> 
>> 
>> I have this little example I have been working on in SimpleITK with the famed cthead1.png data input. Here is a code snippet:
>> 
>> 
>> image = image[(size[0]//2-25):(size[0]//2+25),(size[1]//2-25):(size[1]//2+25)]
>> 
>> 
>> iterps = [sitk.sitkNearestNeighbor,
>>         sitk.sitkLinear,
>>         sitk.sitkBSpline,
>>         sitk.sitkGaussian,
>>         sitk.sitkHammingWindowedSinc,
>>         sitk.sitkCosineWindowedSinc,
>>         sitk.sitkWelchWindowedSinc,
>>         sitk.sitkLanczosWindowedSinc,
>>         sitk.sitkBlackmanWindowedSinc]
>> 
>> eFactor=5
>> 
>> image_list = []
>> 
>> for i in iterps:
>>   image_list.append( sitk.Expand( image, [eFactor]*3, i ))
>> 
>> tiles = sitk.Tile( image_list, [3,0] )
>> 
>> And the following is the output with the different boundary conditions:
>> 
>> http://erie.nlm.nih.gov/~blowek1/images/expand_interp_cbc.png
>> http://erie.nlm.nih.gov/~blowek1/images/expand_interp_zfbc.png
>> 
>> Thanks for you feedback,
>> Brad
>